Question: Solve for $x$ : $6x^2 - 30x - 216 = 0$
Solution: Dividing both sides by $6$ gives: $ x^2 {-5}x {-36} = 0 $ The coefficient on the $x$ term is $-5$ and the constant term is $-36$ , so we need to find two numbers that add up to $-5$ and multiply to $-36$ The two numbers $4$ and $-9$ satisfy both conditions: $ {4} + {-9} = {-5} $ $ {4} \times {-9} = {-36} $ $(x + {4}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x -9) = 0$ $x + 4 = 0$ or $x - 9 = 0$ Thus, $x = -4$ and $x = 9$ are the solutions.